Example

Gypsy moths (Lymantria dispar) are annual insects in which breeding takes place in early to mid summer. After the females lay their eggs, all adults die. The eggs hatch the following spring into larvae that feed on the leaves of tree species, especially species of oaks (Quercus). After a number of larval stages and a pupal stage, the adults emerge. After mating, females lay their eggs and die. Since generation time equals one year, Equations 1.4 or 1.5 may be used. In order to determine population growth in this species, we need to determine R. Assume that a local gypsy moth technician makes annual egg-mass counts in a local forest. She finds that in 2003 there are, on average, 4 gypsy moth egg masses per hectare and each mass contains an average of 40 eggs, for a total of 160 eggs per hectare. When she returns to the same forest in 2004, she finds 5 egg masses with an average of 40 eggs, or a total of 200 eggs per hectare. The local spraying program regulations state that spraying with Bt® (Bacillus thuringiensis) begins whenever egg masses reach 1000 per hectare. Assuming egg-mass density continues to increase at a constant rate, what is the predicted population for the year 2006? In what year would spraying be required?

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